MinT - Best Known (8, 8+6, s)-Nets in Base 16

Best Known (8, 8+6, s)-Nets in Base 16

(8, 8+6, 516)-Net over F₁₆ — Constructive and digital

Digital (8, 14, 516)-net over F₁₆, using

trace code for nets [i] based on digital (1, 7, 258)-net over F₂₅₆, using
- net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(8, 8+6, 578)-Net over F₁₆ — Digital

Digital (8, 14, 578)-net over F₁₆, using

trace code for nets [i] based on digital (1, 7, 289)-net over F₂₅₆, using
- net from sequence [i] based on digital (1, 288)-sequence over F₂₅₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 1 and N(F) ≥ 289, using
    - sharp bound on the number of rational points on curves with genus 1 [i]

(8, 8+6, 50409)-Net in Base 16 — Upper bound on s

There is no (8, 14, 50410)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 72061 555646 958076 > 16¹⁴ [i]